This is still a good feat
TL;DR: the feat is OK for archers even without the -/+ clause. You can decide when to activate that clause. At -5/+5 its not worth to do so in many cases. It still can add damage sometimes, improving the feat slightly.
Value of to hit chance: Decreasing your to hit by 1 decreases your chance to hit by 5% for a normal attack (unless you are at the fringes where only a critical can hit, or where you always hit, and unless advantage/disadvantage are involved). Your expected damage is the probablity to hit times the expected average damage you deal. If you deal less than 20 points of damage on average, then 1 point of to hit is worth less than one point of damage. If you consistently could deal more than 20 damage, then the point of to hit would be worth more.
Base Damage: How much damage does an attack normally deal? Let's assume a longbow with d8 variable damage, a Dexterity contribution of +3 to +5, and a magic weapon contribution of +0 (no such weapon) to +3. This will result in maybe 10 or so damage on a typical attack, a bit less early on, and still under 20 later on. There are of course lots of tricks that you can combine in your builds to deal more damage, but without the static +10 from Sharpshooter, it will be difficult to consistently achieve more than 20 points per attack. At average base damage 10, the value of a point of to hit is about 0.5 points.
Value of added damage: The effective value of +1 point to damage is less than 1, because that damage only gets added to attacks that hit, it is conditional. What is the value? That depends on the to hit chance worsened by activating the feat, and on the armor class of the enemy, which of course varies by enemy. The average to hit chance against level-matched opponents by CR from the Monster Manual is about 70%. It's a bit lower early on, higher at high levels, as the ACs do not grow as fast as the to hit increases. After deducting 5 points to hit, it is about 45%. Archers also can take Achery style for an extra +2 to hit, pushing this up 10%. At average chance to hit with the feat, the value of a point to damage is about 0.45 to 0.55 points.
So on average a point of damage is worth slightly less than a point to hit, and -5/+5 would be a small net loss to damage. Archers (as opposed to Great Weapon Masters) can take Archery style, for a small net gain. When you have optimized your build for higher base damage the loss of to hit is more painful.
Ranged attacks are still boosted
Not only are ranged attacks unrealistically good in D&D. In 5e, except for the disadvantage when shooting at someone right next to you (which you can partially negate by dropping your ranged weapon and as a free object interactions pulling out out an appropriate melee weapon), there is very little downside to them, if any. Maybe that it tends to be harder to find a magical bow than an enchanted sword, but that is really worldbuilding related.
With a ranged fighter and the massive range a longbow affords, you effectively have perfect mobility in most combat situations.
- You can attack any opponent with no risk of being blocked
- You are never unable to reach them because they fly or are on a high ledge
- You run no risk of attacks of opportunity from movement to get into position
- They have no ability to hit back unless they also have ranged weapons of some kind or manage to get close to you
One of the few downsides that remain is the cover that other creatures on the battlefield provide, such as your allies with heavy armor behind whom you can hide. So the ability to ignore cover and long range disadavantage alone is already solid enough to take the feat. In lots of fights this will produce a net improvement of +2 or better to hit.
There is a detailed analysis on the math of the feat. Since you are not forced to apply the -5/+5 shift, you can benefit from it by using it when you have high chances to hit such as when you have advantage and the enemy has low armor class, and avoiding it otherwise. You can use an estimate of their armor, and charts like the ones in the linked analysis to decide when to employ it. For example, if you fight a beast with AC 11, and you have a base +7 to hit and advantage, you would get about 3 points more per hit. In practical play, the swap will give you better results than what you would expect on average. Nobody is forcing you to use the swap, you control this.
Comparison to other feats
You can also compare the feat in its new form the the Spell Sniper feat, which (1) doubles the range on ranged spells. Your ranged weapons very likely already have a ranger much larger than even that, and taking away the disadvantage on long range is maybe comparable. (2) has ranged attacks ignore cover, like this does, and (3) gives you a damage cantrip. Assuming they are a wizard or sorcerer taking Spell Sniper, the cantrip is likely to be Eldritch Blast that deals 1d10 force damage instead of a damage type against which there are more resistances like with Fire Bolt. This is not increasing the damage all the time, just situationally. That seems pretty comparable to the -5/+5 version, and so overall that version seems in line with a comparable feat.
Will players still will want to use it? That will be based on the opinion and preference of each individual player. I would use it if I was playing an archer, and I think your adjustment is a good way to "fix" the feat, if you believe the original feat and sharpshooters are too strong.
Postscriptum: Chart and Usefulness by Tier of Play
This chart that shows the expected damage contribution for an expected base damage of 10, based on what you need to roll to hit with the -5/+5 modifier:
(The weird behavior on the edges is because a 1 always misses, a 20 always hits. If you only can hit on a natural 20, it never hurts to add the swap.)
You can see that with normal attacks, you'll need to hit on a roll of five for it to be worthwhile. Here's how that looks like against monsters from the Monster Manual:
In the beginner levels, you're looking at +2 proficiency bonus, +3 from stat, and very likely +2 from Archery style, for +7 total to hit. Using the swap will be beneficial against any monster with AC 12 or weaker. The average AC of monsters of CR 1/8, 1/4 and 1/2, which you will often fight there, is 12. (In this level range, your base damage is likely 8 points instead of 10, which would mean a 7 on the roll is worth it [chart not shown] and you can use the feat against anything up to AC 14. The average AC for monsters up to CR 4 is 13).
In mid levels, you are looking at +4 from proficiency, +5 from stat, +2 from Archery, and likely +1 from a magic weapon, total +12. Using the swap will be benefical against any moster with AC 17 or weaker. The average AC for monsters of CR 5-16 is 16.
In the highest levels, you are looking at +6 proficiency, +5 stat, +2 Archery, and likely at least +2 magic weapon, total +15. Using the swap wil be benefical against any monster with AC 20 or weaker. The average AC for monsters of CR 17 and up is 20. (Note however that in the base damage here is higher, about 12. This would make it only worthwhile to use the feat on a roll of 3 or better [chart not shown], for monsters of AC 18 or worse. So, Non-Human Person is right that the feat loses some effectiveness at the highest levels.)
For most of the levels where your typcial campaign plays out, using the swap of this version on average still will give you a minuscule benefit, and chosing it selectively should be a useful addition.